Question

Each sweat shop worker at a computer factory can put together 4.7 computers per hour on average with a standard deviation of 0.9 computers. 6 workers are randomly selected to work the next shift at the factory. Round all answers to 4 decimal places where possible and assume a normal distribution.

1. What is the distribution of X? X ~ N(____________,_____________)
2. What is the distribution of ¯x? ¯x ~ N(______________,_____________)
3. What is the distribution of ∑x ? ∑x ~ N(_____________,_____________)
4. If one randomly selected worker is observed, find the probability that this worker will put together between 4.4 and 4.8 computers per hour.
5. For the 6 workers, find the probability that their average number of computers put together per hour is between 4.4 and 4.8.
6. Find the probability that a 6 person shift will put together between 26.4 and 28.8 computers per hour.
7. For part e) and f), is the assumption of normal necessary? Yes No
8. A sticker that says "Great Dedication" will be given to the groups of 6 workers who have the top 20% productivity. What is the least total number of computers produced by a group that receives a sticker? ______________minutes (round to the nearest computer)

Answer 1